Capacitor arrangement assisting method and capacitor arrangement assisting device

ABSTRACT

A capacitor arrangement assisting method wherein data entered by a user, such as the width w of a power supply wiring, the thickness h of a dielectric between the power supply wiring and a ground plane, the ESL cap  of a capacitor, and a target frequency f T  and a target impedance Z T  of an IC, are received, the maximum allowable wiring length l max  of the power supply wiring is calculated on the basis of the received width w of the power supply wiring, the thickness h of the dielectric, the ESL cap  of the capacitor, and the target impedance Z T  of the IC at the target frequency f T , and the calculated maximum allowable wiring length l max  is displayed.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of application Ser. No.13/692,185, filed Dec. 3, 2012, which is a continuation of Internationalapplication No. PCT/JP2011/002872, filed May 24, 2011, which claimspriority to Japanese Patent Application No. 2010-128246, filed Jun. 3,2010, the entire contents of each of which are incorporated herein byreference.

FIELD OF THE INVENTION

The present invention relates to a capacitor arrangement assistingmethod and a capacitor arrangement assisting device.

BACKGROUND OF THE INVENTION

In digital circuits, in order to lower the power supply impedance of adigital IC (hereinafter, simply referred to as an “IC”) and to removenoise, a decoupling capacitor (hereinafter, simply referred to as a“capacitor”) is used on the periphery of a power supply terminal of theIC (for example, see Non-Patent Document 1). Normally, from theviewpoint of suppressing a voltage variation, it is desirable to have alower power supply impedance, and it is thus desirable to have a lowerimpedance of the decoupling capacitor. Therefore, a capacitor having asufficient electrostatic capacitance is used in accordance with a powersupply impedance required by the IC. However, in a high-frequency rangeof several MHz or more, due to the influence of a minute equivalentseries inductance (ESL (Equivalent Series Inductance)) of a capacitor(hereinafter, referred to as an “ESL_(cap)”), impedance is not loweredonly with the electrostatic capacitance. Thus, a capacitor having asmall ESL_(cap) is suitable for a high-frequency range.

In addition, in the high-frequency range, apart from the ESL_(cap), theinductance of a wiring that connects a power supply terminal of the ICwith the capacitor (hereinafter, referred to as an “ESL_(pcb)”) is alsoan issue (for example, see Non-Patent Document 2). Thus, normally, asillustrated in FIG. 13, with the boundary at several MHz (in FIG. 13,approximately 4.3 MHz), the power supply impedance tends to decrease asthe frequency increases in accordance with the electrostatic capacitanceof the capacitor in a lower-frequency side and the power supplyimpedance tends to increase as the frequency increases in ahigher-frequency side. The above-described ESL_(cap) and the ESL_(pcb)are main factors which cause the increase of the impedance in thehigh-frequency side. Thus, in order to achieve a lower power supplyimpedance in the high-frequency range of several MHz or more, theESL_(cap) and the ESL_(pcb) need to be decreased.

Non-Patent Document 1: Takahiro Yaguchi, “Purintohaisenban nopawainteguritei sekkei (Power Integrity Design of PCB),” Journal ofJapan Institute of Electronics Packaging, vol. 12, No. 3, 2009.

Non-Patent Document 2: Tadashi Kubodera, “Kousoku dejitarukairo jissounouhau (High-Speed Digital Circuit Mounting Know-How),” CQ PublishingCo., Ltd., 2002, Chapter 8.

SUMMARY OF THE INVENTION

Since the inductance ESL_(pcb) of a wiring cannot be derived from asimple calculation, the inductance ESL_(pcb) of a wiring is an obstacleto designing for achieving a power supply impedance having a targetvalue (hereinafter, referred to as a “target impedance”) or less.Furthermore, for designing for achieving the power supply impedancehaving the target impedance or less, the arrangement of a capacitor isalso an issue. This is because, since the shape of a wiring thatconnects an IC with a capacitor varies depending on the arrangement ofthe capacitor, the ESL_(pcb) also varies.

Thus, in a conventional method, after the arrangement of a capacitor isonce determined, the power supply impedance is calculated. If the powersupply impedance does not achieve the target impedance, the arrangementof the capacitor is changed, and the power supply impedance iscalculated again. This method needs such a process of trial and error.Furthermore, appropriately changing the arrangement of a capacitor asdescribed above needs a mature technique. Thus, these factors impede thereduction of the development period of electronic circuit boards and thereduction of the cost. Under such circumstances, a technique capable ofsetting an appropriate arrangement of a capacitor more easily without aprocess of trial and error has been desired.

The present invention has been made to solve the above-mentionedproblems. An object of the present invention is to provide a capacitorarrangement assisting method and a capacitor arrangement assistingdevice that are capable of setting an appropriate arrangement of acapacitor more easily without a process of trial and error.

A capacitor arrangement assisting method according to the presentinvention includes a unit inductance calculating step of calculating, onthe basis of the width of a power supply wiring that connects a powersupply terminal of an IC with a capacitor and the thickness of adielectric provided between the power supply wiring and a ground plane,an inductance per unit length of the power supply wiring; and a wiringlength acquiring step of acquiring a wiring length of the power supplywiring that allows a synthetic impedance of an impedance, which iscalculated from an inductance of the power supply wiring set inaccordance with the inductance per unit length of the power supplywiring and the wiring length of the power supply wiring, and animpedance of the capacitor, to be smaller than or equal to a targetimpedance of the IC at a target frequency.

In addition, a capacitor arrangement assisting device according to thepresent invention includes unit inductance calculating means forcalculating, on the basis of the width of a power supply wiring thatconnects a power supply terminal of an IC with a capacitor and thethickness of a dielectric provided between the power supply wiring and aground plane, an inductance per unit length of the power supply wiring;and wiring length acquiring means for acquiring a wiring length of thepower supply wiring that allows a synthetic impedance of an impedance,which is calculated from an inductance of the power supply wiring set inaccordance with the inductance per unit length of the power supplywiring and the wiring length of the power supply wiring, and animpedance of the capacitor, to be smaller than or equal to a targetimpedance of the IC at a target frequency.

In the capacitor arrangement assisting method or the capacitorarrangement assisting device according to the present invention, theinductance per unit length of the power supply wiring is calculated onthe basis of the width of the power supply wiring and the thickness ofthe dielectric provided between the power supply wiring and the groundplane. Thus, the inductance of the power supply wiring can be calculatedeasily without advanced simulation. Furthermore, the wiring length ofthe power supply wiring that allows the synthetic impedance of theimpedance, which is calculated from the inductance of the power supplywiring set in accordance with the inductance per unit length of thepower supply wiring and the wiring length of the power supply wiring,and the impedance of the capacitor, to be smaller than or equal to thetarget impedance of the IC at the target frequency, is acquired. Thatis, the arrangement can be set after a range in which the capacitor canbe arranged is understood. Thus, an appropriate arrangement of thecapacitor can be set more easily without a process of trial and error.Consequently, the development period of a circuit board on which thecapacitor is to be mounted can be reduced, and the development cost canthus be reduced.

In the capacitor arrangement assisting method according to the presentinvention, it is preferable that in the unit inductance calculatingstep, the inductance L₀ (H/m, the same applies to the below)) per unitlength of the power supply wiring is calculated using equation (1):

$\begin{matrix}{{L_{0} = {\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (1)\end{matrix}$

where h (m, the same applies to the below)) represents the thickness ofthe dielectric, w (m, the same applies to the below)) represents thewidth of the power supply wiring, and μ₀ represents the permeability ofa vacuum.

In the capacitor arrangement assisting device according to the presentinvention, it is preferable that the unit inductance calculating meanscalculates the inductance L₀ per unit length of the power supply wiringusing equation (1):

$\begin{matrix}{{L_{0} = {\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (1)\end{matrix}$

where h represents the thickness of the dielectric, w represents thewidth of the power supply wiring, and μ₀ represents the permeability ofa vacuum.

In each case, with the relatively simple equation (1), the inductance L₀per unit length of the power supply wiring can be calculated. Thus, theinductance of the power supply wiring can be calculated more easilywithout advanced simulation.

In the capacitor arrangement assisting method according to the presentinvention, it is preferable that in the unit inductance calculatingstep, the inductance L₀ per unit length of the power supply wiring iscalculated using equation (2):

$\begin{matrix}{{L_{0} = {\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}},} & (2)\end{matrix}$

where h represents the thickness of the dielectric, w represents thewidth of the power supply wiring, and μ₀ represents the permeability ofa vacuum.

In addition, in the capacitor arrangement assisting device according tothe present invention, it is preferable that the unit inductancecalculating means calculates the inductance L₀ per unit length of thepower supply wiring using equation (2):

$\begin{matrix}{{L_{0} = {\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}},} & (2)\end{matrix}$

where h represents the thickness of the dielectric, w represents thewidth of the power supply wiring, and μ₀ represents the permeability ofa vacuum.

In each case, since an advanced power arithmetic operation is notrequired, the inductance per unit length of the power supply wiring canbe calculated more easily.

In the capacitor arrangement assisting method according to the presentinvention, it is preferable that the impedance of the capacitor iscalculated on the basis of an equivalent series inductance of thecapacitor.

In addition, in the capacitor arrangement assisting device according tothe present invention, it is preferable that the impedance of thecapacitor is calculated on the basis of an equivalent series inductanceof the capacitor.

Accordingly, since the impedance of the capacitor can be calculated onlyin view of the equivalent series inductance (ESL_(cap)), an arithmeticoperation can be performed more easily.

A capacitor arrangement assisting method according to the presentinvention includes an input step of receiving input of the width of apower supply wiring that connects a power supply terminal of an IC witha capacitor, the thickness of a dielectric provided between the powersupply wiring and a ground plane, an impedance of the capacitor, and atarget impedance of the IC at a target frequency; a maximum allowablewiring length calculating step of calculating a maximum allowable wiringlength l_(max) (m, the same applies to the below) of the power supplywiring, using equation (3), on the basis of the width w of the powersupply wiring, the thickness h of the dielectric, the impedance Z_(C)(Ω, the same applies to the below) of the capacitor, and the targetimpedance Z_(T) (Ω, the same applies to the below) of the IC at thetarget frequency f_(T) (Hz, the same applies to the below), which areinput in the input step:

$\begin{matrix}{{l_{\max} = \frac{Z_{T} - Z_{c}}{2\pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (3)\end{matrix}$

where μ₀ represents the permeability of a vacuum; and

-   -   a display step of displaying the maximum allowable wiring length        calculated in the maximum allowable wiring length calculating        step.

In addition, a capacitor arrangement assisting device according to thepresent invention includes input means for receiving input of the widthof a power supply wiring that connects a power supply terminal of an ICwith a capacitor, the thickness of a dielectric provided between thepower supply wiring and a ground plane, an impedance of the capacitor,and a target impedance of the IC at a target frequency; maximumallowable wiring length calculating means for calculating a maximumallowable wiring length l_(max) of the power supply wiring, usingequation (3), on the basis of the width w of the power supply wiring,the thickness h of the dielectric, the impedance Z_(C) of the capacitor,and the target impedance Z_(T) of the IC at the target frequency f_(T),which are input by the input means:

$\begin{matrix}{{l_{\max} = \frac{Z_{T} - Z_{c}}{2\pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (3)\end{matrix}$

where μ₀ represents the permeability of a vacuum; and

display means for displaying the maximum allowable wiring lengthcalculated by the maximum allowable wiring length calculating means.

In the capacitor arrangement assisting method or the capacitorarrangement assisting device according to the present invention, whenspecific data including the width of the power supply wiring, thethickness of the dielectric and others are input, the maximum allowablewiring length of the power supply wiring, that is, a range in which thecapacitor can be arranged, can be directly calculated using equation(3), and displayed. Thus, an appropriate arrangement of the capacitorcan be set more easily without a process of trial and error.Consequently, the development period of a circuit board on which thecapacitor is to be mounted can be reduced, and the development cost canthus be reduced.

In the capacitor arrangement assisting method according to the presentinvention, it is preferable that in the maximum allowable wiring lengthcalculating step, the maximum allowable wiring length l_(max) iscalculated using equation (4), instead of equation (3):

$\begin{matrix}{l_{\max} = \frac{Z_{T} - Z_{c}}{2\pi \; f_{T}\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (4)\end{matrix}$

In the capacitor arrangement assisting device according to the presentinvention, it is preferable that the maximum allowable wiring lengthcalculating means calculates the maximum allowable wiring length l_(max)using equation (4), instead of equation (3):

$\begin{matrix}{l_{\max} = \frac{Z_{T} - Z_{c}}{2\pi \; f_{T}\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (4)\end{matrix}$

In each case, since an advanced power arithmetic operation is notrequired, the maximum allowable wiring length can be acquired moreeasily.

In the capacitor arrangement assisting method according to the presentinvention, it is preferable that in the maximum allowable wiring lengthcalculating step, the maximum allowable wiring length is calculatedbased on equation (5):

$\begin{matrix}{{\frac{1}{2\pi \frac{\mu_{0}}{\pi}} = {0.4 \times 10^{6}}},} & (5)\end{matrix}$

where μ₀ represents the permeability of a vacuum (4π×10⁻⁷).

In addition, in the capacitor arrangement assisting device according tothe present invention, it is preferable that the maximum allowablewiring length calculating means calculates the maximum allowable wiringlength based on equation (5):

$\begin{matrix}{{\frac{1}{2\; \pi_{\pi}^{\mu_{0}}} = {0.4 \times 10^{6}}},} & (5)\end{matrix}$

where μ₀ represents the permeability of a vacuum (4π×10⁻⁷).

Accordingly, since an arithmetic operation for calculating the maximumallowable wiring length is more simplified, an arithmetic operation canbe performed more easily.

In the capacitor arrangement assisting method according to the presentinvention, it is preferable that in the maximum allowable wiring lengthcalculating step, the maximum allowable wiring length is calculated onthe basis of the impedance Z_(C) of the capacitor using equation (6):

Z_(C)=2πfESL_(cap)   (6),

where ESL_(cap) represents an equivalent series inductance of thecapacitor.

In addition, in the capacitor arrangement assisting device according tothe present invention, it is preferable that the maximum allowablewiring length calculating means calculates the maximum allowable wiringlength on the basis of the impedance Z_(C) of the capacitor usingequation (6):

Z_(C)=2πfESL_(cap)   (6),

where ESL_(cap) represents an equivalent series inductance of thecapacitor.

Accordingly, since the maximum allowable wiring length can be calculatedonly in view of the equivalent series inductance (ESL_(cap)) regardingthe impedance of the capacitor, an arithmetic operation can be performedmore easily.

According to the present invention, an appropriate arrangement of acapacitor can be set more easily without a process of trial and error.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating the configuration of a capacitorarrangement assisting device according to a first embodiment.

FIG. 2 illustrates an example of a power supply wiring.

FIG. 3 is a diagram for explaining synthetic impedance.

FIG. 4 is a diagram illustrating the maximum allowable wiring length ofthe power supply wiring.

FIG. 5 is a flowchart illustrating the processing procedure of a wiringlength acquiring process by the capacitor arrangement assisting deviceaccording to the first embodiment.

FIG. 6 is a block diagram illustrating the configuration of a capacitorarrangement assisting device according to a second embodiment.

FIG. 7 is a flowchart illustrating the processing procedure of a maximumallowable wiring length calculating process by the capacitor arrangementassisting device according to the second embodiment.

FIG. 8 is a graph illustrating measurement results in Example 1.

FIG. 9 is a graph illustrating measurement results in Example 2.

FIG. 10 is a graph illustrating measurement results in Example 3.

FIG. 11 is a graph illustrating measurement results in Example 4.

FIG. 12 is a graph illustrating measurement results in Example 5.

FIG. 13 is a graph illustrating the frequency characteristics of powersupply impedance.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, preferred embodiments of the present invention will beexplained in detail with reference to the drawings. In each of thedrawings, the same elements are referred to with the same referencesigns and redundant explanations will be omitted.

First Embodiment

First, referring to FIG. 1, the configuration of a capacitor arrangementassisting device 1 according to a first embodiment will be explained.FIG. 1 is a block diagram illustrating the configuration of thecapacitor arrangement assisting device 1.

The capacitor arrangement assisting device 1 assists designing of acircuit board by presenting a range in which a decoupling capacitor canbe arranged (power supply wiring length) so as to achieve a targetimpedance or less, on the basis of specific data, such as the width of apower supply wiring and the thickness of a dielectric between the powersupply wiring and a ground plane. To this end, the capacitor arrangementassisting device 1 includes an input unit 10, an information processingunit 20, and a display unit 30. The information processing unit 20includes a unit inductance calculating part 21 and a wiring lengthacquiring part 22. Hereinafter, the configuration of each of the unitswill be explained in detail.

Here, the case where a capacitor 120 is arranged on a power supplywiring 100 illustrated in FIG. 2 will be explained as an example. Thepower supply wiring 100 is formed of, for example, copper foil or thelike. The power supply wiring 100 is formed in a microstrip line shapefor the ground plane with the dielectric (board) therebetween. The widthof the power supply wiring 100 is represented by w, and the thickness ofthe dielectric provided between the power supply wiring 100 and theground plane (the distance in the board thickness direction between thepower supply wiring 100 and the ground plane) is represented by h. Apower supply terminal 110 a of a digital IC 110 and a first terminal 120a of the capacitor 120 are connected with the power supply wiring 100. Asecond terminal 120 b of the capacitor 120 is connected with the groundplane with a via 130 therebetween.

The capacitor 120 supplies electric power necessary for the operation ofthe IC 110 and removes noise intruding via the power supply wiring 100and noise generated by the operation of the IC 110. Here, the capacitor120 has an electrostatic capacitance large enough to lower the impedancein a low-frequency range of several MHz or less and has an ESL_(cap)that impedes the reduction of the impedance in a high-frequency range ofseveral MHz or more. In addition, a target impedance Z_(T) that isrequired for the power supply of the IC 110 and an upper-limit frequencythat achieves the target impedance Z_(T) (target frequency f_(T)) aredisclosed in advance.

The input unit 10 includes, for example, a keyboard or a touch panel.The input unit 10 receives data entered by a user, such as the width w(m, the same applies to the below) of the power supply wiring 100, thethickness h (m, the same applies to the below) of the dielectric betweenthe power supply wiring 100 and the ground plane, the impedance Z, (Ω,the same applies to the below) of the capacitor 120 (or the ESL_(cap)(H, the same applies to the below), and the target frequency f_(T) (Hz,the same applies to the below) and the target impedance Z_(T) (Ω, thesame applies to the below) of the IC 110. These data may be entered andstored in a memory in advance.

The information processing unit 20 calculates a range in which thecapacitor 120 can be arranged (wiring length) in accordance with anarithmetic expression on the basis of the data, such as the width w ofthe power supply wiring 100 and the thickness h of the dielectric,received from the input unit 10. The information processing unit 20includes a microprocessor that performs arithmetic processing forreceived input data, a ROM that stores a program (including anarithmetic expression) for causing the microprocessor to executeindividual processing and data, a RAM that temporarily stores variousdata such as arithmetic results, and the like. In the informationprocessing unit 20, when the program stored in the ROM is executed bythe microprocessor, functions of the unit inductance calculating part 21and the wiring length acquiring part 22 are implemented.

The unit inductance calculating part 21 calculates the inductance L₀(H/m, the same applies to the below) per unit length of the power supplywiring 100, using equation (1), on the basis of the cross-section sizeof the power supply wiring 100 that connects the power supply terminal110 a of the IC 110 with the capacitor 120, that is, the width w of thepower supply wiring 100 and the thickness h of the dielectric:

$\begin{matrix}{{L_{0} = {\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (1)\end{matrix}$

where μ₀ represents the permeability of a vacuum.

That is, the unit inductance calculating part 21 functions as a unitinductance calculating means. The calculated inductance L₀ per unitlength of the power supply wiring 100 is output to the wiring lengthacquiring part 22.

The wiring length acquiring part 22 calculates a synthetic impedance(hereinafter, also referred to as a “power supply impedance) Z_(all) (Ω,the same applies to the below) of the impedance Z_(P), which iscalculated on the basis of the inductance of the power supply wiring 100set in accordance with the inductance L₀ per unit length of the powersupply wiring 100 and the wiring length l (m, the same applies to thebelow) of the power supply wiring 100, and the impedance Z_(C) of thecapacitor 120. The wiring length acquiring part 22 also acquires thewiring length l of the power supply wiring 100 that allows thecalculated synthetic impedance Z_(all) to be smaller than or equal tothe target impedance Z_(T) of the IC 110 at the target frequency f_(T).That is, the wiring length acquiring part 22 functions as a wiringlength acquiring means. This will be explained later in more detail.

A high-frequency portion of the power supply impedance Z_(all) (Ω, thesame applies to the below) of the IC 110 can be approximated with theimpedance obtained by series connection of the impedance Z_(P) (Ω, thesame applies to the below) of the power supply wiring 100, whichconnects the IC 110 with the capacitor 120, with the impedance Z_(C) ofthe capacitor 120. Here, when the capacitor 120 is connected, in ahigh-frequency range in which the length of the power supply wiring 100is sufficiently shorter than the wavelength, the impedance Z_(P) of thepower supply wiring 100 can be approximated with a value obtained bymultiplying the inductance L₀ per unit length of the power supply wiring100 by the wiring length l (m, the same applies to the below) of thepower supply wiring 100. This is because the capacitor 120 is consideredto be short-circuited in a high-frequency range of several MHz or more.

Thus, when the power supply impedance Z_(all) is calculated only in viewof the magnitude of the impedance, based on equation (1), a result isobtained as equation (7):

$\begin{matrix}{Z_{all} = {{Z_{p} + Z_{c}} = {{2\; \pi \; f\; l\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}} + Z_{c}}}} & (7)\end{matrix}$

When the wiring length of the power supply wiring 100 (the distancebetween the capacitor 120 and the power supply terminal 110 a of the IC110) l is obtained by transforming equation (7), a result is obtained asequation (8):

$\begin{matrix}{l = \frac{Z_{all} - Z_{c}}{2\; \pi \; f\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (8)\end{matrix}$

As is clear from equation (8), in order to make the power supplyimpedance Z_(all) to be smaller than the target impedance Z_(T) at thetarget frequency f_(T), the wiring length l of the power supply wiring100 is set to be smaller than or equal to the maximum allowable wiringlength l_(max) (m, the same applies to the below) in equation (3):

$\begin{matrix}{l_{m\; {ax}} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (3)\end{matrix}$

That is, as illustrated in FIG. 4, by setting the wiring length l of thepower supply wiring 100 to be smaller than or equal to the maximumallowable wiring length l_(max) calculated using equation (3), thearrangement of the capacitor 120 can be set in such a manner that thepower supply impedance is smaller than or equal to the target impedanceZ_(T).

Here, when a value (4π×10⁻⁷) is substituted for μ₀, the obtained valueis expressed as a round number, and equation (3) is simplified, equation(9) is obtained:

$\begin{matrix}{l_{m\; {ax}} \cong {0.4\frac{Z_{T} - Z_{c}}{{f_{T}\left( \frac{h}{w} \right)}^{0.6}} \times 10^{6}}} & (9)\end{matrix}$

In addition, in a high-frequency range of several MHz or more, since theimpedance Z_(C) of the capacitor 120 is considered to be governed by theESL_(cap) (H, the same applies to the below), the impedance Z_(C) can berepresented by equation (6):

Z_(C)=2πfESL_(cap)   (6)

Here, when equation (6) is reflected in equation (3), equation (10) isobtained:

$\begin{matrix}{l_{m\; {ax}} = \frac{Z_{T} - {2\; \pi \; f_{T}{ESL}_{cap}}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (10)\end{matrix}$

Meanwhile, when equation (6) is reflected in equation (9), equation (11)is obtained:

$\begin{matrix}{l_{m\; {ax}} \cong {0.4\frac{Z_{T}2\; \pi \; f_{T}{ESL}_{cap}}{{f_{T}\left( \frac{h}{w} \right)}^{0.6}} \times 10^{6}}} & (11)\end{matrix}$

Thus, also by calculating the maximum allowable wiring length l_(max)using equation (9), (10), or (11), which is a more simplified equation,instead of equation (3), and arranging the capacitor 120 in such amanner that the wiring length l of the power supply wiring 100 issmaller than or equal to the maximum allowable wiring length l_(max),the power supply impedance can be designed to be smaller than or equalto the target impedance Z_(T). The calculated maximum allowable wiringlength l_(max) is output to the display unit 30.

The display unit 30 includes, for example, an LCD display or the like.The display unit 30 displays input data received by the input unit 10and calculation results, such as the maximum allowable wiring lengthl_(max).

The operation of the capacitor arrangement assisting device 1 and acapacitor arrangement assisting method will now be explained withreference to FIG. 5. FIG. 5 is a flowchart illustrating the processingprocedure of a wiring length acquiring process by the capacitorarrangement assisting device 1.

In step S100, data entered by a user, such as the width w of the powersupply wiring 100, the thickness h of the dielectric between the powersupply wiring 100 and the ground plane, the impedance Z_(C) of thecapacitor 120 (or the ESL_(cap)), and the target frequency f_(T) and thetarget impedance Z_(T) of the IC 110, are received.

In step S102 (corresponding to a unit inductance calculating step), theinductance L₀ per unit length of the power supply wiring 100 iscalculated, using equation (1), on the basis of the width w of the powersupply wiring 100, which connects the power supply terminal 110 a of theIC 110 with the capacitor 120, and the thickness h of the dielectric,which are received in step S100:

$\begin{matrix}{L_{0} = {\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (1)\end{matrix}$

In step S104 (corresponding to a wiring length acquiring step), first, asynthetic impedance (power supply impedance) Z_(all) of the impedanceZ_(P), which is calculated from the inductance of the power supplywiring 100 set in accordance with the inductance L₀ per unit length ofthe power supply wiring 100 calculated in step S102 and the wiringlength l of the power supply wiring 100, and the impedance Z_(C) of thecapacitor 120 is calculated. Then, the wiring length l of the powersupply wiring 100 that allows the calculated synthetic impedance Z_(all)to be smaller than or equal to the target impedance Z_(T) of the IC 110at the target frequency f_(T) is acquired.

More specifically, first, when the synthetic impedance Z_(all) iscalculated on the basis of the inductance L₀ per unit length of thepower supply wiring 100 (equation (1)), equation (7) is obtained:

$\begin{matrix}{Z_{all} = {{Z_{p} + Z_{c}} = {{2\; \pi \; f\; l\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}} + Z_{c}}}} & (7)\end{matrix}$

Next, when equation (7) is transformed to calculate the wiring length lof the power supply wiring 100, equation (8) is obtained:

$\begin{matrix}{l = \frac{Z_{all} - Z_{c}}{2\; \pi \; f\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (8)\end{matrix}$

Then, the maximum allowable wiring length l_(max) of the wiring length lof the power supply wiring 100, which is required to make the powersupply impedance. Z_(all) to be smaller than the target impedance Z_(T)at the target frequency f_(T), is acquired from equation (3):

$\begin{matrix}{l_{m\; {ax}} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (3)\end{matrix}$

In step S104, the maximum allowable wiring length l_(max) of the wiringlength l may be acquired using equation (9), (10), or (11), which is amore simplified equation, instead of equation (3).

In step S106, results including the maximum allowable wiring lengthl_(max) acquired in step S104 are displayed (see FIG. 4).

According to this embodiment, the inductance L₀ per unit length of thepower supply wiring 100 is calculated on the basis of the width w of thepower supply wiring 100 and the thickness h of the dielectric providedbetween the power supply wiring 100 and the ground plane. Thus, theinductance of the power supply wiring 100 can be easily acquired withoutadvanced simulation. Furthermore, the wiring length l of the powersupply wiring 100 that allows the synthetic impedance Z_(all) of theimpedance Z_(P), which is calculated from the inductance of the powersupply wiring 100 set in accordance with the inductance L₀ per unitlength of the power supply wiring 100 and the wiring length l of thepower supply wiring 100, and the impedance Z_(C) of the capacitor 120 tobe smaller than or equal to the target impedance Z_(T), of the IC 110 atthe target frequency f_(T), can be acquired. That is, the arrangementcan be set after a range in which the capacitor 120 can be arranged isunderstood. Thus, an appropriate arrangement of the capacitor 120 can beset more easily without a process of trial and error. Consequently, thedevelopment period of a circuit board on which the capacitor 120 is tobe mounted can be reduced, and the development cost can thus be reduced.

Furthermore, according to this embodiment, with a relatively simpleequation (1), the inductance L₀ per unit length of the power supplywiring 100 can be acquired. Thus, the inductance of the power supplywiring 100 can be acquired more easily without advanced simulation.

Furthermore, according to this embodiment, since the impedance of thecapacitor 120 can be replaced with equation (6), the impedance of thecapacitor 120 can be calculated only in view of the ESL_(cap), and amore simple arithmetic operation can be achieved.

A variation of the first embodiment will now be explained. When aprecision is not relatively required, equation (1) can be simplified toequation (2):

$\begin{matrix}{L_{0} = {\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (2)\end{matrix}$

Thus, the inductance L₀ per unit length of the power supply wiring 100may be calculated using equation (2), instead of equation (1).

Furthermore, when the above-mentioned individual equations (3), (7),(8), and (9) to (11) are transformed on the basis of equation (2),equations provided below can be obtained. That is, equation (7) istransformed into equation (12):

$\begin{matrix}{Z_{all} = {{Z_{p} + Z_{c}} = {{2\; \pi \; f\; l\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}} + Z_{c}}}} & (12)\end{matrix}$

Equation (8) is transformed into equation (13):

$\begin{matrix}{l = \frac{Z_{all} - Z_{c}}{2\; \pi \; f\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (13)\end{matrix}$

Equation (3) is transformed into equation (4):

$\begin{matrix}{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (4)\end{matrix}$

Equation (9) is transformed into equation (14):

$\begin{matrix}{l_{\max} \cong {0.4\frac{Z_{T} - Z_{c}}{f_{T}\sqrt{\frac{h}{w}}} \times 10^{6}}} & (14)\end{matrix}$

Equation (10) is transformed into equation (15):

$\begin{matrix}{l_{\max} = \frac{Z_{T} - {2\; \pi \; f_{T}{ESL}_{cap}}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (15)\end{matrix}$

Equation (11) is transformed into equation (16):

$\begin{matrix}{l_{\max} \cong {0.4\frac{Z_{T} - {2\; \pi \; f_{T}{ESL}_{cap}}}{f_{T}\sqrt{\frac{h}{w}}} \times 10^{6}}} & (16)\end{matrix}$

Thus, the maximum allowable wiring length l_(max) may be calculatedusing any one of equations (4) and (14) to (16), instead of equation(3).

According to this variation, since an advanced power arithmeticoperation is not required, an arithmetic operation can be performed moreeasily.

Second Embodiment

The configuration of a capacitor arrangement assisting device 2according to a second embodiment will now be explained with reference toFIG. 6. FIG. 6 is a block diagram illustrating the configuration of thecapacitor arrangement assisting device 2. In FIG. 6, components the sameas or similar to those in the first embodiment will be referred to withthe same reference signs.

The capacitor arrangement assisting device 2 differs from the capacitorarrangement assisting device 1 described above in that the informationprocessing unit 20 includes a maximum allowable wiring lengthcalculating part 23, instead of the unit inductance calculating part 21and the wiring length acquiring part 22. Since the other features of theconfiguration are the same as or similar to those of the capacitorarrangement assisting device 1 described above, a detailed explanationwill be omitted here. In this embodiment, the input unit 10 functions asan input means, and the display unit 30 functions as a display means.

The maximum allowable wiring length calculating part 23 calculates themaximum allowable wiring length l_(max) of the power supply wiring 100,using equation (3), on the basis of the width w of the power supplywiring 100, the thickness h of the dielectric provided between the powersupply wiring 100 and the ground plane, the impedance Z_(C) of thecapacitor 120 (or the ESL_(cap)), and the target impedance Z_(T) of theIC 110 at the target frequency f_(T), which are input from the inputunit 10:

$\begin{matrix}{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (3)\end{matrix}$

That is, the maximum allowable wiring length calculating part 23functions as a maximum allowable wiring length calculating means.

The maximum allowable wiring length l_(max) may be calculated usingequation (9), (10), or (11), which is a more simplified equation,instead of equation (3). In addition, calculation results including thecalculated maximum allowable wiring length l_(max) and others aredisplayed by the display unit 30.

The operation of the capacitor arrangement assisting device 2 and acapacitor arrangement assisting method will now be explained withreference to FIG. 7. FIG. 7 is a flowchart illustrating the processingprocedure of a maximum allowable calculating process by the capacitorarrangement assisting device 2.

In step S200, data entered by a user, such as the width w of the powersupply wiring 100, the thickness h of the dielectric between the powersupply wiring 100 and the ground plane, the impedance Z_(C) of thecapacitor 120 (or the ESL_(cap)), and the target frequency f_(T) and thetarget impedance Z_(T) of the IC 110, are received.

In step S202 (corresponding to a maximum allowable wiring lengthcalculating step), the maximum allowable wiring length l_(max) of thepower supply wiring 100 is calculated, using equation (3) (or equation(9), (10), or (11)), on the basis of the width w of the power supplywiring 100, the thickness h of the dielectric, the impedance Z_(C) ofthe capacitor 120 (or the ESL_(cap)), and the target impedance Z_(T) ofthe IC 110 at the target frequency f_(T), which are received in stepS200:

$\begin{matrix}{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}} & (3)\end{matrix}$

A designer can design the power supply impedance to be smaller than orequal to the target impedance Z_(T) by arranging the capacitor 120 insuch a manner that the wiring length l is smaller than or equal to themaximum allowable wiring length l_(max).

In step S204, results including the maximum allowable wiring lengthl_(max) calculated in step S202 and others are displayed (see FIG. 4).

According to this embodiment, when specific data including the width wof the power supply wiring 100 and the thickness h of the dielectric andothers are input, the maximum allowable wiring length l_(max) of thepower supply wiring 100, that is, a range in which the capacitor 120 canbe arranged, is directly calculated using equation (3) and displayed.Thus, an appropriate arrangement of the capacitor 120 can be set moreeasily without a process of trial and error. Consequently, thedevelopment period of a circuit board on which the capacitor 120 is tobe mounted can be reduced, and the development cost can thus be reduced.

Furthermore, according to this embodiment, by expressing thepermeability μ₀ of a vacuum as a round number and simplifying equation(3), an arithmetic equation to be used for calculating the maximumallowable wiring length l_(max) can be more simplified, and anarithmetic operation can be performed more easily.

According to this embodiment, by replacing the impedance Z_(C) of thecapacitor 120 with equation (6), the impedance of the capacitor 120 canbe calculated only in view of the ESL_(cap). Thus, an arithmeticoperation can be performed more easily.

Here, in order to confirm effects of the capacitor arrangement assistingdevice 2 or the capacitor arrangement assisting method according to thisembodiment, the maximum allowable wiring length l_(max) was calculatedby changing the width w of the power supply wiring 100, the thickness hof the dielectric, the target frequency f_(T), and the target impedanceZ_(T). In addition, the capacitor 120 was arranged in accordance withthe calculation results, and the power supply impedance was measured(Examples 1 to 5). FIGS. 8 to 12 illustrate measurement results of theimpedance in the Examples 1 to 5. In the graphs illustrated in FIGS. 8to 12, the horizontal axis represents frequency (MHz) and the verticalaxis represents impedance (Ω). A monolithic ceramic capacitor of 1 μFwas used in measurement. Furthermore, in arithmetic operations, theESL_(cap) was set to 0.6 nH, and the maximum allowable wiring lengthl_(max) was calculated using equation (11):

$\begin{matrix}{l_{\max} \cong {0.4\frac{Z_{T} - {2\; \pi \; f_{T}{ESL}_{cap}}}{{f_{T}\left( \frac{h}{w} \right)}^{0.6}} \times 10^{6}}} & (11)\end{matrix}$

EXAMPLE 1

In Example 1, a four-layer multilayer board was assumed. The powersupply wiring 100 whose width w was 1 mm and whose distance to theground plane (thickness of the dielectric) h was 0.4 mm, was designed insuch a manner that the target frequency f_(T) was 150 MHz and the targetimpedance Z_(T) was smaller than or equal to 2Ω. In a calculation resultby equation (11), the maximum allowable wiring length l_(max) wascalculated to be 6.6 mm. In accordance with this result, in themeasurement, the capacitor 120 was arranged at the position 6.0 mm awayfrom the power supply terminal 110 a of the IC 110. As a result, themeasured power supply impedance was 1.9Ω at 150 MHz, as illustrated inFIG. 8, and it was confirmed that the measured power supply impedancewas smaller than or equal to the target impedance Z_(T).

EXAMPLE 2

In Example 2, a double-sided board was assumed. The power supply wiring100 whose width w was 1 mm and whose distance to the ground plane(thickness of the dielectric) h was 1.2 mm, was designed in such amanner that the target frequency f_(T) was 50 MHz and the targetimpedance Z_(T) was smaller than or equal to 1.5Ω. In a calculationresult by equation (11), the maximum allowable wiring length l_(max) wascalculated to be 9.4 mm. In accordance with this result, in themeasurement, the capacitor 120 was arranged at the position 9.0 mm awayfrom the power supply terminal 110 a of the IC 110. As a result, themeasured power supply impedance was 1.4Ω at 50 MHz, as illustrated inFIG. 9, and it was confirmed that the measured power supply impedancewas smaller than or equal to the target impedance Z_(T).

EXAMPLE 3

In Example 3, a six-layer multilayer board was assumed. The power supplywiring 100 whose width w was 2 mm and whose distance to the ground plane(thickness of the dielectric) h was 0.2 mm, was designed in such amanner that the target frequency f_(T) was 100 MHz and the targetimpedance Z_(T) was smaller than or equal to 1Ω. In a calculation resultby equation (11), the maximum allowable wiring length l_(max) wascalculated to be 9.9 mm. In accordance with this result, in themeasurement, the capacitor 120 was arranged at the position 9.0 mm awayfrom the power supply terminal 110 a of the IC 110. As a result, themeasured power supply impedance was 0.9Ω at 100 MHz, and it wasconfirmed that the measured power supply impedance was smaller than orequal to the target impedance Z_(T).

EXAMPLE 4

In Example 4, a power supply wiring through which large current passeswas assumed. The power supply wiring 100 whose width w was 5 mm andwhose distance to the ground plane (thickness of the dielectric) h was0.2 mm, was designed in such a manner that the target frequency f_(T)was 70 MHz and the target impedance Z_(T) was smaller than or equal to0.8Ω. In a calculation result by equation (11), the maximum allowablewiring length l_(max) was calculated to be 21.1 mm. In accordance withthis result, in the measurement, the capacitor 120 was arranged at theposition 21.0 mm away from the power supply terminal 110 a of the IC110. As a result, the measured power supply impedance was 0.73Ω at 70MHz, and it was confirmed that the measured power supply impedance wassmaller than or equal to the target impedance Z_(T).

EXAMPLE 5

In Example 5, a power supply wiring through which much larger currentpasses was assumed. The power supply wiring 100 whose width w was 10 mmand whose distance to the ground plane (thickness of the dielectric) hwas 0.2 mm, was designed in such a manner that the target frequencyf_(T) was 80 MHz and the target impedance Z_(T) was smaller than orequal to 0.7Ω. In a calculation result by equation (11), the maximumallowable wiring length l_(max) was calculated to be 20.8 mm. Inaccordance with this result, the capacitor was arranged at the position21.0 mm away from the power supply terminal 110 a of the IC 110. As aresult, the measure power supply impedance was 0.67Ω at 80 MHz, and itwas confirmed that the measured power supply impedance was smaller thanor equal to the target impedance Z_(T). As described above, according tothis embodiment, it was confirmed that appropriate maximum allowablewiring lengths l_(max) can be acquired for various cross-section sizes(the width w and the thickness h of the dielectric) and the targetimpedances Z_(T).

As described above, when a precision is not relatively required,equation (1) can be simplified to equation (2):

$\begin{matrix}{L_{0} = {\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (2)\end{matrix}$

With equation (2), equation (11) can be transformed into equation (16):

$\begin{matrix}{l_{\max} \cong {0.4\frac{Z_{T} - {2\; \pi \; f_{T}{ESL}_{cap}}}{f_{T}\sqrt{\frac{h}{w}}} \times 10^{6}}} & (16)\end{matrix}$

Thus, the maximum allowable wiring length l_(max) may be calculatedusing equation (16).

Here, comparison between results of calculation of the maximum allowablewiring length l_(max) under the conditions of Examples 1 to 5 describedabove using equation (16) (for distinction, hereinafter, referred to asthe “maximum allowable wiring length l_(max)2”) and results ofcalculation using equation (11), will be illustrated in Table 1.

TABLE 1 Conditions h Z_(T) f_(T) l_(max) l_(max)2 Difference W (mm) (mm)(Ω) (MHz) (mm) (mm) l_(max)2/l_(max) Example 1 1 0.4 2 150 6.6 6.0 0.90Example 2 1 1.2 1.5 50 9.4 9.5 1.01 Example 3 2 0.2 1 100 9.9 7.8 0.79Example 4 5 0.2 0.8 70 21.0 15.2 0.72 Example 5 10 0.2 0.7 80 20.7 14.00.68

As illustrated in Table 1, in the case of the maximum allowable wiringlength l_(max)2, which can be calculated by a simpler arithmeticoperation, a calculation result tends to be a little smaller than acalculation result for the maximum allowable wiring length l_(max).However, in the case where the capacitor 120 is arranged on the basis ofthe maximum allowable wiring length l_(max)2, the power supply impedancetends to be smaller, that is, tends to be on the safer side. Thus, thecalculation result of the maximum allowable wiring length l_(max)2 isallowable.

As described above, in the case of using equation (16), althoughprecision is slightly lower than the case using equation (11), anarithmetic operation can be easily performed. Thus, an appropriatearrangement of the capacitor 120 can be set more easily.

Although embodiments of the present invention have been described above,the present invention is not limited to the embodiments described above.Various changes may be made to the present invention. For example, in avariation of the second embodiment, the maximum allowable wiring lengthl_(max)2 is calculated using equation (16). However, equation (4), (14),or (15) may be used, instead of equation (16). Furthermore, for example,the shape of the power supply wiring 100 and the like are not limited tothe embodiments described above.

REFERENCE SIGNS LIST

1,2 capacitor arrangement assisting device

10 input unit

20 information processing unit

21 unit inductance calculating part

22 wiring length acquiring part

23 maximum allowable wiring length calculating part

30 display unit

100 power supply wiring

110 IC

120 capacitor

130 via

1. A capacitor arrangement assisting method comprising: receiving aninput of a width of a power supply wiring that connects a power supplyterminal of an IC with a capacitor, a thickness of a dielectric providedbetween the power supply wiring and a ground plane, an impedance of thecapacitor, and a target impedance of the IC at a target frequency;calculating a maximum allowable wiring length of the power supply wiringon the basis of the width of the power supply wiring, the thickness ofthe dielectric, the impedance of the capacitor, and the target impedanceof the IC at the target frequency; and displaying the maximum allowablewiring length.
 2. The capacitor arrangement assisting method accordingto claim 1, wherein the maximum allowable wiring length l_(max) iscalculated as follows: $\begin{matrix}{{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (3)\end{matrix}$ where μ₀ represents the permeability of a vacuum, wrepresents the width of the power supply wiring, h represents thethickness of the dielectric, Z_(C) represent the impedance of thecapacitor, and Z_(T) represents the target impedance of the IC at thetarget frequency f_(T).
 3. The capacitor arrangement assisting methodaccording to claim 1, wherein the maximum allowable wiring lengthl_(max) is calculated as follows: $\begin{matrix}{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}} & (4)\end{matrix}$ where μ₀ represents the permeability of a vacuum, wrepresents the width of the power supply wiring, h represents thethickness of the dielectric, Z_(C) represent the impedance of thecapacitor, and Z_(T) represents the target impedance of the IC at thetarget frequency f_(T).
 4. The capacitor arrangement assisting methodaccording to claim 1, wherein the maximum allowable wiring length iscalculated as follows: $\begin{matrix}{\frac{1}{2\; \pi \frac{\mu_{0}}{\pi}} = {0.4 \times 10^{6}}} & (5)\end{matrix}$ where μ₀ represents the permeability of a vacuum.
 5. Thecapacitor arrangement assisting method according to claim 1, wherein themaximum allowable wiring length is calculated on the basis of theimpedance Z_(C) of the capacitor as follows:Z_(C)=2πfESL_(cap), where ESL_(cap) represents an equivalent seriesinductance of the capacitor.
 6. A capacitor arrangement assisting devicecomprising: an input unit that receives input of a width of a powersupply wiring that connects a power supply terminal of an IC with acapacitor, a thickness of a dielectric provided between the power supplywiring and a ground plane, an impedance of the capacitor, and a targetimpedance of the IC at a target frequency; a maximum allowable wiringlength calculating unit that calculates a maximum allowable wiringlength of the power supply wiring on the basis of the width of the powersupply wiring, the thickness of the dielectric, the impedance of thecapacitor, and the target impedance of the IC at the target frequency;and a display unit that configures the maximum allowable wiring lengthcalculated by the maximum allowable wiring length calculating unit fordisplay.
 7. The capacitor arrangement assisting device according toclaim 6, wherein the maximum allowable wiring length calculating unitcalculates the maximum allowable wiring length l_(max) as follows:$\begin{matrix}{{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\left( \frac{h}{w} \right)^{0.6}}},} & (3)\end{matrix}$ where μ₀ represents the permeability of a vacuum, wrepresents the width of the power supply wiring, h represents thethickness of the dielectric, Z_(C) represent the impedance of thecapacitor, and Z_(T) represents the target impedance of the IC at thetarget frequency f_(T).
 8. The capacitor arrangement assisting deviceaccording to claim 6, wherein the maximum allowable wiring lengthcalculating unit calculates the maximum allowable wiring length l_(max)as follows: $\begin{matrix}{{l_{\max} = \frac{Z_{T} - Z_{c}}{2\; \pi \; f_{T}\frac{\mu_{0}}{\pi}\sqrt{\frac{h}{w}}}},} & (4)\end{matrix}$ where μ₀ represents the permeability of a vacuum, wrepresents the width of the power supply wiring, h represents thethickness of the dielectric, Z_(C) represent the impedance of thecapacitor, and Z_(T) represents the target impedance of the IC at thetarget frequency f_(T).
 9. The capacitor arrangement assisting deviceaccording claim 6, wherein the maximum allowable wiring lengthcalculating unit calculates the maximum allowable wiring length asfollows: $\begin{matrix}{{\frac{1}{2\; \pi \frac{\mu_{0}}{\pi}} = {0.4 \times 10^{6}}},} & (5)\end{matrix}$ where μ₀ represents the permeability of a vacuum.
 10. Thecapacitor arrangement assisting device according to claim 6, wherein themaximum allowable wiring length calculating unit calculates the maximumallowable wiring length on the basis of the impedance Z_(C) of thecapacitor as follows:Z_(C)=2πfESL_(cap), where ESL_(cap) represents an equivalent seriesinductance of the capacitor.